The mass flow of a fluid can be determined by measuring its volume flow and applying a density factor to the volume measurement. In the past, an average density was adequate for most applications and separate measurement of density was not required. However, in a propulsion system using cryogenic propellent, such as liquid hydrogen, the density of the cryogenic propellent under steady or transient flow conditions is an important parameter relating to the performance and reliability of the system. Thus, high accuracy of instantaneous density measurement is often required.
The density of a cryogenic fluid in the liquid phase, such as liquid hydrogen follows the equation of the state of the fluid and is primarily a function of temperature, and to a lesser extent, of pressure. This relationship, however, is not always applicable if the fluid is in a two-phase flow containing vapor or supercritical state. The quality of the cryogenic fluid is an additional consideration since vapor content can substantially alter the overall fluid density value.
The theoretical characterization of the fluid density in terms of dielectric constant and refractive index gained impetus in physics due to the Lorentz-Lorentz formulation, and the subsequent developments in dielectric theory due to Onsager, Van Vleck, Froelich, Kirkwood, Langevin-Debye, et al. One dielectric formula which is conspicuously notable in such evaluation is the Clausius-Mossotti equation, despite its early origin and later coexistance with the Onsager formula. The Clausius-Mossotti formula is considered conceptually applicable to non-polar spherical molecules, of which certain liquid gases or cryogenic fluids are examples.
Among the experimental techniques utilizing the dielectric approach, the Clausius-Mossotti ratio has been applied to instrument the density of cryogenic propellents and its multiphase fluid mechanics in aerospace technology. In low temperature physics investigations, high speed analog-type computational dielectric measurement has been applied earlier by researchers to probe into the dynamic phase transitional phenomena of liquid gases, including observations on the period-doubling transients of the bifurcation cascade.
Most of the previously reported methods were either of non-computational or analog computer type design. As such, rigorous applications of pertinent theoretical parameters was neither implemented nor emphasized. However, recent low temperature research--e.g. in the areas of space science, chaos research and liquid hydrogen bubble chamber applications--requires greater conceptual rigor in order to optimize the measurement uncertainties and resolution. The instant invention utilizes a rigorous solution of the molecular Clausius-Mossotti formula by bridging the gap between the macroscopic and molecular dielectric theory using a dielectric susceptibility parameter; and, in combination with a high-speed microprocessor based electronics system to overcome the problems inherent with the current analog measurements.
A search of the prior art did not disclose any patents that read on the claims of the instant invention. However, U.S. Pat. No. 3,421,077, issued Feb. 7, 1969, to Frederick F. Liu, who is also the inventor of the instant invention, is considered related. The U.S. Pat. No. 3,421,077 patent discloses an analog system that measures the density of a cryogenic fluid by sensing the fluid's dielectric properties. The dielectric-to-density converter and electronics of the U.S. Pat. No. 3,421,077 patent differ from the present invention as does the mechanization of the Clausius-Mossotti equation. One noteable difference in the prior art equation is that the proportionally term K is treated as a constant, whereas in the instant invention, the K term is variable and is compensated by computer solution of the dielectric parameter of .epsilon.-1.